Ahmad Halimi Razlighi, Mohammad Siddiqur Rahman, Maximilian H. V. Tillmann +2eess.SP cs.LG eess.IV stat.ML
Multi-Task semantic communication (SemCom) prioritizes simultaneous execution of multiple tasks over bit-accurate reconstruction in future intelligent networks. In our prior work [1], we introduced the cooperative multi-task SemCom (CMT-SemCom) framework, in which the semantic encoder is divided into a common unit (CU) and multiple specific units (SUs) to facilitate cooperative multi-task processing. However, CMT-SemCom has been evaluated on homogeneous classification tasks on simplistic datasets, limiting its applicability to real-world perception systems. In this paper, we extend our CMT-SemCom to jointly handle heterogeneous classification and regression tasks on the complex Cityscapes dataset. We adopt the information maximization (InfoMax) principle so that it accommodates mixed discrete and continuous semantic variables. In particular, we benchmark the proposed framework against independent single-task training, a conventional task-agnostic digital transmission, and single-encoder multi-decoder SemCom. Additionally, we investigate the impact of CU capacity on joint task performance, providing design insights. Extensive evaluations demonstrate that CMT-SemCom significantly outperforms the benchmarks.
We introduce Xiaomi-TabLDM, a tabular large data foundation model for classification and regression via in-context learning, which delivers superior prediction accuracy without requiring task-specific fine-tuning. Pretrained exclusively on synthetic data generated from structural causal models (SCMs), our model enables more flexible context utilization and more efficient capacity scaling. i) A new performance standard. Strong regression performance across benchmarks: Xiaomi-TabLDM ranks 1st on OpenML-CTR23 and 2nd on regression across TALENT, TabArena, and BCCO, demonstrating consistently strong regression performance across four complementary benchmark suites. Favorable performance--efficiency trade-off: Xiaomi-TabLDM combines strong predictive performance with substantially lower computational cost. For example, on TabArena regression, it achieves the second-highest Elo while using 82% less training time and 68% less prediction time than the top-ranked TabFM. ii) Large-scale synthetic pretraining. Xiaomi-TabLDM expands the coverage and diversity of synthetic tabular data used for pretraining. We also adopt a three-stage training strategy together with dual-stream feature grouping, lightweight Attention Residual, and sparse Mixture-of-Experts, enabling Xiaomi-TabLDM to learn richer feature interactions and expert specialization across diverse tabular tasks. iii) Test-time scaling. Xiaomi-TabLDM further extends tabular prediction through test-time compute scaling, where allocating additional computation at inference time consistently improves predictive performance over the base model.
Zain Ul Abidin, Habeeban Memon, Junaid Ahmedcs.AI cs.CV
Accurate through-thickness measurement of subsurface delamination depth in Carbon Fiber Reinforced Polymer (CFRP) is important for structural assessment because defect location determines affected load-bearing layers. Optical pulsed thermography (OPT) provides a two-dimensional thermal video rather than volumetric measurements, so depth must be inferred from temporal heat-diffusion responses. A challenge is spatial dataset bias: when calibration defects follow regular grids, regression models may memorize their geometry instead of learning physical relationship between thermal decay and depth. This work introduces a spatio-temporal decoupling architecture that separates spatial defect localization from temporal depth measurement. Defect regions are first localized using segmentation methods, after which thermal responses are spatially averaged and converted into sixteen physics-informed temporal, energy, statistical, and geometric features. These features expose the one-dimensional heat-conduction relationship while withholding pixel coordinates from the depth model. Four regression models are evaluated using specimen-level cross-validation: Random Forest (RF), Gradient Boosting Machine (GBM), Advanced Multi-Layer Perceptron (Adv-MLP), and XGBoost. Unregularized trees and over-parameterized Adv-MLP exhibit calibration collapse under geometric shifts, with errors exceeding 0.5 mm. In contrast, regularized XGBoost with L1/L2 penalties and column sampling maintains cross-specimen calibration, achieving a mean absolute error (MAE) of 0.056 mm and root mean square error (RMSE) of 0.085 mm. Predicted depths are merged with masks to generate Delaunay-triangulated three-dimensional defect models in three to five seconds per specimen. Results show that mathematical regularization and spatio-temporal decoupling reduce spatial memorization in thermal-video depth regression.
The classification and regression of particle collision events constitute a persistent computational challenge in experimental high energy physics, where large volumes of simulated data must be processed with both speed and precision. This work carries out a systematic comparison of four classical machine learning architectures, support vector machines (SVM), artificial neural networks (ANN), convolutional neural networks (CNN), and long short-term memory (LSTM) networks against their quantum counterparts: quantum SVM (QSVM), quantum neural networks (QNN), quantum CNN (QCNN), and quantum LSTM (QLSTM). All models are trained on simulated proton-proton collision events with electron-positron and muon-antimuon final states from the CERN Open Data portal, using transverse-momentum components as input features and transverse-momentum magnitude as the regression target. Classical architectures, and in particular the CNN and LSTM, achieve marginally better quantitative performance under current hardware and dataset constraints. Quantum models, however, reach competitive accuracy with substantially fewer trainable parameters: the QCNN reproduces the performance of the deep classical CNN using only four qubits and a circuit of depth three, pointing to a genuine parameter-efficiency advantage on near-term quantum devices. A baseline analysis confirms that the regression problem is non-trivial for shallow polynomial fits, supporting the relevance of the architectural comparison. These results characterize the trade-offs between classical and quantum approaches under realistic, resource-constrained conditions and provide a benchmark for future studies on actual quantum hardware.
EXAONE Tabular is a compact tabular foundation model family for classification and regression via in-context learning, producing predictions without dataset-specific gradient updates. Pretrained exclusively on a synthetic structural-causal-model (SCM) prior, its central contribution is an architecture-centered redesign of tabular in-context learning. Rather than compressing features into a fixed row embedding before a separate row-level learner, EXAONE Tabular interleaves feature-axis attention within each item with support-conditioned item-axis attention within each feature at every Transformer layer, mediated by item-summary and feature-summary tokens. Across four public benchmarks, EXAONE Tabular combines strong predictive performance with high efficiency. On TabArena, its 20.81M-parameter classification model ranks first overall, surpassing tuned ensembles and 4-hour AutoML pipelines, while regression reaches the performance regime of the 1.64B-parameter TabFM at roughly 1/11 the inference cost. On BCCO and TALENT, EXAONE Tabular ranks second in classification and first in regression. On ScoringBench, it achieves the best mean rank for both point-estimation and predictive-distribution quality, leading the $R^2$, RMSE, and CRPS evaluations. Together, these results establish EXAONE Tabular as a state-of-the-art compact tabular foundation model family, combining strong predictive performance across classification, point regression, and probabilistic regression with an efficient model design.
Functional data analysis is an important statistical field that treats data as random functions. In practice, the random functions are often not fully observed but instead measured at discrete times. While simpler problems, such as mean and covariance estimation, have been widely studied for discretely observed data, optimal estimation of linear regression for this data type has remained unsolved for over two decades. To tackle this fundamental challenge, we propose a novel approach, referred to as pooling ridge estimation, which combines the advantages of pooling strategy and RKHS-based method by incorporating the unbiased estimation of operators based on discretely observed measurements from all subjects. This unified estimation framework enables us to achieve minimax optimality in prediction risk in arbitrary sampling schemes ranging from sparse to dense designs, for both scalar-on-function and function-on-function regression models. Such methodological and theoretical advances are obtained for the first time and accurately reveal the influence of discrete sampling. For scalar-on-function regression, the phase transition occurs once, separating the convergence behavior into two distinct regimes. Remarkably, for function-on-function regression, up to three phase transitions may occur, determined by the sampling frequencies of the predictor/response functions. Finally, simulation experiments and two real data examples provide empirical support for the proposed methods.
Understanding how neural networks learn and organize features is central to understanding their behavior. Much existing theory of feature learning has focused on the emergence of a global low-dimensional predictive geometry. We show that this picture is incomplete. In regression problems with clustered data, we demonstrate that multilayer perceptrons (MLPs) naturally develop monosemantic specialized neurons: individual neurons become strongly aligned with a specific predictive feature relevant to a particular region of the input space. Rather than learning a single global low-dimensional representation, MLPs learn a collection of local low-dimensional representations that can collectively span a high-dimensional space. This specialization provably gives MLPs a data-efficiency advantage over feature-learning methods based on a global low-dimensional representation.
Gazi Abdur Rakib, Tristan Ashton, Ryan A. Loomis +4stat.ME cs.LG
We introduce a new class of regression models for scan statistics on real-valued signals. These allow for improved fitting of non-stationary signals to contrast with the interval anomalies identified by the scan statistics. Our models can represent generalized likelihood ratio statistics. While these methods naively require $O(n^4)$ for a length $n$ signal, we provide algorithmic improvements which lead to linear time algorithms (with assumptions on max interval width). Our methods, especially ones based on Nadaraya-Watson kernel regression, are demonstrated as especially effective in detecting both synthetically planted anomalies, and for identifying a real ``platforming'' issue in interferometric astronomy.
Khivishta Boodhoo, Josh Plumbly, Nicholas Watsoncs.LG cs.AI
Rising energy demand, fossil fuel depletion and climate change highlight the need for more efficient energy production and consumption. Offshore oil and gas platforms face challenges related to inefficient energy use, system failures, accessibility and environmental impact. Machine learning (ML) offers opportunities to improve the safety, sustainability and efficiency of these systems; however, previous research has largely focused on increasing oil production rather than reducing energy consumption on platforms. This study investigates the use of ML and search algorithms to improve diesel efficiency on an offshore oil platform. Data collected over 18 months from a platform in Scotland were analysed, focusing on four diesel generators as the primary diesel-consuming equipment. Following exploratory data analysis and outlier detection, regression models were developed to predict daily diesel consumption for different generator power loads. Multiple Linear Regression and Artificial Neural Networks achieved the best predictive performance compared with Extra Trees Regression, Extreme Gradient Boosting and Random Forest. Search algorithms were then used to identify combinations of generator power loads that minimised daily diesel consumption. The results showed an average diesel saving of 27% per day compared with the worst daily power-load combinations, equivalent to approximately 24,000 litres/day. These findings demonstrate significant opportunities for improving energy efficiency on offshore oil platforms using ML-based optimisation.
Vehicular traffic is a major source of air pollution; however, the contribution of remotely acquired traffic information to local machine-learning (ML) air-pollution models remains insufficiently characterised. This study evaluates four interpretable tree-based ML models (Random Forest, Extra Trees, LightGBM, and XGBoost) under six predictor scenarios combining progressively larger predictor sets, ranging from remotely acquired traffic, meteorological, and temporal variables alone to the inclusion of measurements from one and four neighbouring monitoring stations, to estimate NO$_2$, PM$_{10}$, PM$_{2.5}$, and O$_3$ concentrations across several sites in London. ML model performance was compared with a ridge linear regression model as a baseline, with spatial interpolation methods and with a cross-site validation experiment. When modelling without data from neighbouring stations, the RMSE for NO$_2$ ranged from 9.73 to 11.66 $μ$g/m$^3$ without traffic information, compared with 8.72 to 11.52 $μ$g/m$^3$ when traffic information was included. Additionally, for NO$_2$, SHAP analyses indicate that traffic-related variables can contribute at levels comparable to pollutant measurements from neighbouring monitoring stations in traffic-dominated~environments.
Pablo M. Berná, Antonio Falcó, Diego Mondéjarcs.LG math.FA
We develop constructive approximation and learning guarantees for shallow neural models with infinite-dimensional inputs observed through finitely many coordinates. The analysis is based on a parameter-normalized neural dictionary and its associated weighted variation class. Within this class, the approximation error separates into a distribution-dependent coordinate-truncation term and a greedy finite-width term. For empirical regression, a fully-corrective greedy procedure yields population guarantees whose statistical complexity is uniform in the retained input resolution. The same framework extends to Hilbert-valued responses without an explicit dependence on the output dimension. The dimension-free statements are statistical, not computational: selecting a new neuron still requires solving a nonconvex parameter-search problem. The quasi-Polish construction underlying recent infinite-dimensional universal approximation results provides a motivating example, and synthetic experiments illustrate the predicted resolution, width, and sample-size regimes.
This paper investigates the estimation of the regression operator in function-on-function regression models. While traditional research has predominantly focused on linear models or their immediate nonlinear extensions, we propose a neural operator approach to accommodate general regression operators under mild smoothness assumptions. Operator learning has emerged as an active area of machine learning, particularly for solving physical models governed by partial differential equations. Using this paradigm, our methodology introduces the separable neural operator, a neural-operator architecture that represents the regression operator through input-dependent coefficient functions and output-dependent basis functions. Beyond adapting this architecture to the regression operator estimation problem, we establish the consistency of the estimator under relatively mild smoothness and sampling conditions, allowing functional data to be observed on dense, possibly irregular, discrete grids. We also apply the proposed approach to the BGC Argo data and demonstrate its potential for oceanographic research.
Whether input-dependent ("dynamic") combination of a regression model pool beats the best static blend depends on the shift and is rarely known before deployment. Can a small labeled target-domain probe tell us when reallocating trust across regions of the input space will pay off? We answer this with $\widehat{D}_{\mathrm{CF5}}$, which estimates from the probe the cross-fitted gain of the regionwise convex combination over the best static convex blend: the realizable value of deciding, region by region, whom to trust. Across a frozen suite of 12 dataset-shift pairs (spatial, temporal, domain, feature-cluster), $\widehat{D}_{\mathrm{CF5}}$ predicts realized regionwise test gains with dataset-level Spearman $+0.98$ (95% CI $[+0.83, +1.00]$; $p=5\times10^{-5}$), including two cases overturning preregistered expectations. The relationship holds in a 16-pair sensitivity analysis (Spearman $+0.83$), whereas alternative probe diagnostics reach at most $+0.66$. This contrast isolates regional trust reallocation: correlation is $+0.98$ for regionwise-convex gain, but $+0.01$ for smooth covariate-dependent stacking after affine correction. A controlled generator shows dynamic gains arise from the interaction of shift heterogeneity and local competence, increase with shift severity, and become realizable between 128 and 256 probe labels in the tested grid. The Probe-Validated Ensemble Selector chooses among a static affine stacker and dynamic realizers, deploying a candidate only when a held-out lower confidence bound clears the static-convex floor. In a preregistered prospective batch, it matched or improved the floor in all 12 runs; two deployments reduced test risk by 11% and 16%, while the gate rejected a candidate whose un-gated deployment incurred $>30\times$ the static loss. We release OpenRegShift, a reproducible evaluation harness for regression ensembles under distribution shift.
Eve Harling, Chattarin Pumtako, Bernd Porr +2eess.IV cs.LG
Background: Accurate body composition analysis using Computed Tomography (CT) scans is essential for assessing skeletal muscle area (SMA) and skeletal muscle density (SMD), key markers of nutritional status in cancer patients. Conventional manual methods are labour-intensive and require specialist expertise, limiting their routine clinical use. Therefore, this study serves as a feasibility and pilot investigation to explore the potential of deep learning-based automated regression for body composition analysis within a clinical workflow. Methods: Four deep learning architectures (AlexNet, UNet, GoogLeNet, and ResNet34) were trained to predict SMA, SMD, subcutaneous fat area (SFA), and visceral fat area (VFA) from CT scans of colorectal cancer patients. Systematic hyperparameter optimization identified the most accurate models, which were subsequently implemented in a web application for clinical use. Results: GoogLeNet achieved the best performance, with a mean percentage error (PE) of 4.96% for SMA prediction, while AlexNet reached 8.12% for SMD. Independent testing demonstrated robust accuracy, correctly classifying body composition metrics in 80% of cases. The web application delivered rapid and consistent outputs, supporting integration into clinical workflows. Conclusion: Optimized deep learning models, particularly GoogLeNet and AlexNet, can automate CT-derived body composition analysis with a Mean Percentage Error (PE) of 4.96% for SMA and 8.12% for SMD. These tools have the potential to streamline clinical practice by reducing the time and expertise required for manual segmentation. Further validation in larger, more diverse datasets is warranted.
Hyewook Kim, Byul Kang, Seokbin Yoon +1cs.CV cs.LG
Air traffic controllers perceive traffic complexity through the radar display, suggesting that a computer vision model operating on the same imagery may provide a natural architecture for modeling controller-perceived complexity; however, whether radar imagery is a viable input format for deep learning vision models remains unclear. Unlike natural images, radar images are extremely sparse and self-similar, consisting primarily of a black background and a few visually identical aircraft blobs, while small changes in aircraft positions can substantially alter sector-level complexity. To test whether a vision model can capture these operationally important differences, we encode each traffic situation as a position image supplemented by five channels representing aircraft state variables, including heading, speed, and altitude, and train a Vision Transformer (ViT) to regress four intrinsic complexity components derived from pairwise geometric relations among aircraft. The model achieves $R^2 > 0.96$ for all four components, and a one-aircraft-removal perturbation study shows that its response changes proportionally to how much the removed aircraft contributed to sector complexity rather than treating every removal as equivalent. These results demonstrate that, despite its atypical visual characteristics, radar imagery is a viable input format for air traffic complexity modeling.
In real-world scenarios, the training data usually contains redundant features, label noise and feature noise, which provide severe challenges for the efficiency of machine learning methods. Since standard support vector machine (SVM) adopts $l_2$-norm penalty and hinge loss function, it lacks the ability of selecting significant features and is sensitive to noise. To address these issues, this paper proposes a novel asymmetric, robust, bounded, sparse and smooth (aR) loss function for $l_1$-norm penalized geometric twin SVM (aRSGTSVM) to handle classification and regression tasks. The $l_1$-norm penalty can achieve the feature selection. The proposed aR loss function can not only effectively mitigate the impact of label noise, but also significantly enhance the stability to resampling noise, i.e., the zero-mean feature noise around the boundary hyperplanes. Furthermore, a statistical analysis of the robustness of aRSGTSVM was also conducted using the influence function. Since aRSGTSVM involves nonconvex and nonsmooth optimization, we develop a fast and stable proximal gradient descent based solving algorithm. Compared with related state-of-the-art methods, experimental results demonstrate the superiority of the proposed aRSGTSVM on both synthetic and UCI datasets. Furthermore, we apply aRSGTSVM to index tracking tasks, where results for tracking the different indices in the China stock market show that it can achieve satisfactory performance.
Pre-trained black-box predictive functions encode knowledge distilled from massive datasets and extensive computation. However, when the available input features differ from those the black box expects, direct use is infeasible. We introduce a method for transferring predictive knowledge from the black box to a new, heterogeneous input space. Our approach decomposes the target regression function into a transferable component, which the black box can inform, and a non-transferable component, which captures information unique to the new space. We propose a two-step neural network procedure, estimating the transferable component from abundant unlabeled feature pairs that bridge the two input spaces and the non-transferable component from limited labels. We derive prediction risk bounds that improve on those of a non-transfer alternative when the non-transferable component is small or smooth, and the procedure adapts to either case. Under additional conditions, the worst-case risk of our estimator is of strictly smaller polynomial order than the minimax risk of estimation from the labeled data alone. We extend the framework to multiple black boxes, each on its own input space, and show that aggregation can reduce prediction error relative to the best single black box. Simulated and real data demonstrate the practical value of the method.
Fernando Garcia de la Cruz, David López-Ayala, Pablo Zinemanas +2eess.AS cs.AI eess.SP
AI-generated music is increasingly used at the stem level, with producers integrating synthetic drums, basslines, or vocals alongside human-performed instruments. However, current AI music detection systems are binary, treating tracks as either fully AI or fully human. In this paper, we reformulate AI music detection as a regression problem on a continuous AI energy ratio, alpha in [0, 1]. We propose a methodology that leverages a multi-track music dataset to assemble mixtures of human-performed and AI-reconstructed stems (obtained using a neural audio codec) with known proportions of each content type. Using this approach, we first show that a CNN-based model trained on fully AI-generated or human-performed tracks, which achieves >99% accuracy as a binary detector, when faced with mixed content, yields an output that rises with the AI stems' energy contribution, acting as a noisy and miscalibrated estimator. Our analysis of the influence of different stems shows that detection sensitivity depends on the instrument and reflects its frequency content: drums and guitar carry strong codec-artifact signatures, while vocals and bass are less detectable. Based on these insights, we train a similar CNN-based model for regression of alpha, achieving MAE = 0.076 and R^2 = 0.85 on held-out mixtures from the same pipeline. These results suggest that the regression formulation is an initial promising step towards AI-music detection in realistic music production workflows.
Adulteration of bovine milk using urea remains a major food quality and health concern, motivating the development of rapid and quantitative screening tools. Conventional approaches, including laboratory-based analytical methods and spectroscopic techniques, have been used for urea detection; however, many remain less suitable for rapid, low-cost routine screening due to requirements such as specialized instrumentation, sample preparation, chemical reagents, or laboratory operation. This study introduces a pragmatic, cost-effective, accurate, and laboratory-validated MSI-based method for quantitative urea estimation under controlled density conditions using a multispectral-imaging-based regression framework. An in-house-built multispectral imaging system operating in twelve discrete spectral bands (365--940~nm) was used to acquire multispectral images of milk samples prepared with controlled urea addition and water for density balancing. Fresh milk was obtained on the day of image acquisition, and the specific gravity of the milk was verified to be 1.032 at 20°C using a hydrometer. Multiple linear regression provided an initial mapping with a high validation $R^2$ of 0.9599, while a feed-forward neural network further improved predictive performance with a validation $R^2$ of 0.9773. These results demonstrate the feasibility of transmittance multispectral imaging for accurate, non-destructive urea quantification under controlled density-balanced conditions, supporting its potential as a rapid screening approach for milk-quality assessment.
Chansophea Wathanak In, Yi Li, Wai Ming Tai +1cs.DS cs.LG
This paper studies active regression for single-index models under general $\ell_p$-loss with an unknown $1$-Lipschitz link function $f$, formulated as $\min_{f,x} \|f(Ax)-b\|_p^p$ with full access to $A$ but coordinate-query access to $b$. Prior work established upper bounds for known link functions for all $p\geq 1$ and for unknown link functions only in the $p=2$ case, together with lower bounds for $p\leq 2$. This work addresses the more challenging setting of unknown link functions and general $p \geq 1$. A non-adaptive sampling algorithm is presented that achieves a $(1+ε)$-approximation using $O(d^{p/2\vee 1}/ε^{p\vee 2}\operatorname{poly}\log(n/ε))$ queries. Nearly tight lower bounds are also established for $p>2$. These results close much of the remaining gap in active $\ell_p$-regression for single-index models.
Viacheslav Barkov, Jonas Schmidinger, Robin Gebbers +1cs.LG
Visible and near-infrared (vis-NIR) and mid-infrared (MIR) spectroscopy enable rapid, cost-effective prediction of soil properties. Yet, translating high-dimensional, highly collinear spectra into accurate soil property predictions remains challenging, particularly when employing machine learning. We systematically investigated regression models and dimensionality reduction approaches for spectroscopic modeling across 85 regression tasks from open benchmark datasets in pedometrics spanning field-scale digital soil mapping and a global soil spectral library. We compared an in-context learning tabular foundation model (TabPFN), a convolutional neural network (CNN), rule-based regression (Cubist), Random Forest, and partial least squares regression (PLSR) using full spectra as well as features derived from principal component analysis (PCA) and partial least squares (PLS) latent variables. TabPFN consistently delivered the best overall performance across scales, including large spectral library tasks with tens of thousands of soil samples. Notably, TabPFN applied directly to full spectra already surpassed all classical baselines, showing that explicit dimensionality reduction is not strictly required for strong performance. Further improvements were achieved through PLS, which proved to be an effective dimensionality reduction strategy for all models. Combining PLS latent variables with TabPFN yielded the best predictions overall. Our findings provide evidence-based guidance for spectroscopic calibration model selection across operational scales, demonstrating that the long-standing advantages of PLSR and modern tabular foundation models complement each other in chemometrics.
Music is often used as a medium for communicating emotion, with performers shaping perceived affect through interpretation. This study addresses the challenge of identifying and predicting subtle changes in perceived emotion that are exclusively due to differences in performance. We focus on classical solo piano music, using a set of 6 commercial recordings of Bach's Well-Tempered Clavier Book I, annotated in terms of valence and arousal. By encoding the recordings through performance-specific features only, we isolate performance information from aspects of the composition itself, which tend to dominate the overall perceived emotional category. A preliminary analysis validates that these features vary meaningfully across performers. We then propose a relative regression framework, Delta-VA, to predict deviations in valence-arousal relative to an ``average'' performance, thereby focusing on the changes in emotion brought about by a specific way of playing a piece. In addition to the standard $R^2$ regression score, we introduce geometric evaluation metrics to assess the preservation of pairwise differences between performances. Results indicate high directional consistency with the ground truth, but also a compression in prediction magnitude, indicating that the model tends to underestimate expressive performance effects.
Jacobus G. M. van der Linden, Mim van den Bos, Emir Demirovićcs.LG cs.AI
Optimal decision trees (ODTs) are compact, interpretable machine learning models that globally optimize a given objective, but their scalability remains challenging. While recent work has proposed a variety of search strategies to improve scalability, the precise contribution of each strategy remains unclear. To address this gap, we introduce a general algorithmic framework for ODTs that instantiates previously used search strategies and enables the definition of new ones. This provides a common lens through which to understand and compare different strategies, which we use to empirically investigate the effect of 18 search strategies. Compared to the state of the art, the best strategy in our evaluation achieves significantly better anytime performance for classification, and improves runtime by more than an order of magnitude for regression.
We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems. It is shown that the proposed extension - that we coin as Entropy-Optimal Manifold Regression (EOMR) - allows a robust learning with linearly-scaling iteration and memory complexities. EOMR is compared to the most complete set of state-of-the-art tools from the Artificial Intelligence (AI) and Machine Learning (ML) that is available to the author, on the very challenging problems from chaotic and fluid dynamics: (i) on predicting the Lorenz-96 systems dynamics in strongly- and very-strongly chaotic regimes (with forcing parameter being $F=8$ and $F=12$, respectively); and, (ii) on a data from the Hasegawa-Wakatani model on the edge of the tokamak plasma. It is demonstrated that the proposed benchmarks (i) and (ii), indeed, are the very challenging problems for the state of the art ML and AI tools - since both the general-purpose gradient boosted random forests and deep neuronal networks, as well as transformer-based AI tools like TabPFN v.03 (more spezialised for large-dimensional small data learning problems) - result in orders of magnitude inferior root mean squared prediction errors, and orders of magnitude larger model complexities, when compared to the EOMR. For a Hasegawa-Wakatani example, EOMR distills a very simple entropy-optimal and skilful description of the leading Essential Orthogonal Function (EOF) dynamics, given by linear, causal and weakly-stationary autoregressive process described by just 8 parameters.
We present a novel approach to regression tasks using classification which is motivated by the mechanism used by fruitflies to sense their environment. Specifically, we formulate a general framework for learning nonlinear input-output relationships by replacing complex global surrogate models with a finite library of representative local patterns. Since scientific data often occupy limited and recurring regions of the input space, we generate predictions by measuring similarities between a query and stored patterns, then combining their associated responses through weighted reconstruction. We apply this approach to nonlinear dynamical systems, data-driven regression, and physics-informed learning using suitable embeddings and similarity measures. For dynamical systems, our offline-online workflow extracts patterns from data or governing equations during the offline phase, while online prediction requires only similarity evaluation and response aggregation. This structure helps us reduce computational and memory demands while providing explicit control over the trade-off among accuracy, storage, and inference cost.
Keith G. Mills, Aedan J. DeFrates, Joong Ho Kimcs.LG
Graph Neural Networks (GNN) facilitate effective prediction on graph data such as molecules, media networks and neural network blueprints. GNNs facilitate prediction through message passing techniques which define how information flows from a node to its neighbors. Due to the ubiquity of the graph data type, the development of newer and better GNNs has garnered much interest in the machine learning community. However, GNN evaluation and benchmarking is primarily driven by classification tasks. Thus, prospective GNN message passing layers are evaluated on their ability to outperform prior work in classification contexts. In contrast, GNNs are equally capable of performing scalar regression prediction, yet this class of problem is often overlooked when proposing new GNNs while the best classification GNNs are utilized in an a priori or off-the-shelf manner for regression problems. In response, this paper studies the efficacy of GNN layers in a slew of regression contexts from rank ordering, error minimization and insight extraction. Results show that deep convolutional GNNs, particularly GEN, are more effective at these tasks than attention-based GNNs, while other classical, theoretically-inspired GNNs remain competitive and efficient.
Lawrence Fulton, Christopher Fulton, Arvind Sharma +1stat.ME cs.LG math.DG stat.AP
Regression estimates from observational data can depend on specification under multicollinearity, while sequential sums of squares (SS) depend on term order. We introduce Retrospective Orthogonal Design (ROD), which reconstructs conditional mean surfaces on a probability-balanced lattice. ROD preserves observed cell means, completes unsupported cells, applies weighted tensor-product contrasts, and evaluates the reconstructed surface through piecewise-affine interpolation over Freudenthal polyhedra. Resolution and completion are selected jointly by validation among rank-admissible candidates, followed by refitting and evaluation on an untouched test set. For an admissible lattice, $\mathbf{X}^{\top}\mathbf{W}\mathbf{X}=c\mathbf{I}$, yielding specification-invariant contrast effects and unique, order-independent SS within the retained contrast space. Response-free projection calibration maps the fixed reconstruction onto a declared scientific basis and corrects finite-resolution recovery loss. Across 6,480 simulation conditions spanning nine data-generating processes, ROD matched or exceeded polynomial regression in five processes and performed strongest on threshold, sign-interaction, and localized surfaces. For the quadratic-interaction process, mean out-of-sample $R^2$ differed by only $0.0001$, while calibrated coefficient bias remained small across prespecified targets. A Rao-based information adjustment provides dependence-aware sample-size guidance for ROD planning. In a weighted Mincer application, ROD produced the highest out-of-sample $R^2$ point estimate, with substantial interval overlap with polynomial regression, and provided exhaustive SS allocations invariant to term-entry order.
Parth G. Dangi, Yogesh Kumaar Meenacs.HC cs.AI cs.ET
Brain-machine interfaces (BMIs) can assist individuals with limited mobility, such as stroke survivors or amputees. One of the key challenges in developing BMIs is expanding their usability and control, which can be achieved by accurately decoding multiple kinematic and kinetic parameters. To address this, we propose three regression models: partial least squares regressor, multilayered perceptron, and attention based regressor, to decode multiple movement parameters from EEG signals. We evaluated these models on the WAY EEG GAL dataset, focusing on their performance under subject specific and subject independent conditions with two strategies: a single model for all parameters and a baseline with separate models for each parameter. Among all regressors, the attention based regressor achieved the best performance, with an $R^2$ of 0.8 and a latency of 29.2 milliseconds, demonstrating significant improvement in simultaneous multi parameter decoding. However, its performance dropped for single parameter decoding. The multi layered perceptron showed more consistent but lower accuracy across both decoding types ($R^2$ = 0.49). These findings highlight the potential of attention based models for real time multi command BMI systems and contribute to the development of more intuitive control devices.
Distributional random forests replace mean-based CART splitting with criteria that compare the full conditional response distribution in candidate children. We implement and systematically study a family of such criteria inside a single honest-forest implementation: isotropic random-Fourier-feature maximum mean discrepancy (MMD), an anisotropic diagonal-bandwidth variant, an adaptive per-split frequency-selection variant, and a non-kernel sliced-Wasserstein criterion, together with post-hoc kernel-mean shrinkage of the forest weights. Using paired-seed comparisons across synthetic quantile mechanisms, real univariate benchmarks, a California-housing subsample curve, and multivariate synthetic and real responses, we characterize where each extension pays. Three findings recur. First, among distributional criteria ordinary isotropic MMD is already close to best in class: the anisotropic, adaptive-frequency, and sliced-Wasserstein extensions, and post-hoc shrinkage, do not systematically improve on it. Second, on scalar tabular regression mean-based CART splitting remains the robust default and wins many cells. Third, multivariate responses are the regime where distributional splitting clearly earns its keep, most sharply on a pure-dependence copula where the energy score separates the criteria even though marginal CRPS does not. The evidence supports a simple allocation story: distributional splitting helps only when non-location structure is both present and estimable; otherwise it dilutes split-selection power away from the mean. All criteria, the honest forest, and the paired-comparison harness are implemented in the open-source \texttt{drforest} library, whose Rust-backed split search makes broad criterion sweeps inexpensive.
Cayan Deniz Kucuktopana, Javier Fumanal-Idocin, Richard Pitts +1cs.LG
Machine learning models achieve high predictive accuracy in regression tasks, but their deployment in safety-critical and regulated domains requires interpretability. While fuzzy rule-based systems offer transparent, linguistically explicit interpretable models, Mamdani-style fuzzy regression remains underrepresented in modern machine learning software libraries. This paper presents an interpretable regression extension for the Ex-Fuzzy library, enabling Mamdani fuzzy inference with scalar consequents learned directly from data. For this, a target-aware partition initialisation strategy based on Fuzzy C-Means clustering is introduced, in which linguistic variables are derived from an augmented input-output space to emphasise output-relevant regions of the feature space. The proposed extension is evaluated on ten regression datasets from the KEEL repository, comparing Gaussian and trapezoidal partition strategies against standard baselines including linear regression, multilayer perceptron, and random forests. Experimental results show that Gaussian partitions consistently outperform uniform trapezoidal partitions, achieving a mean coefficient of determination of approximately 0.86 while producing compact rule bases of 10-15 human-readable rules. The proposed implementation provides a transparent and competitive alternative to black-box regression models, supporting practical interpretability with competitive predictive performance.